Variable spectral efficiency optical modulation schemes

ABSTRACT

A transmitter of a communications system includes a first encoder configured to apply a shaping operation to a data signal to generate a shaped data signal, a second encoder configured to encode the shaped data signal according to a forward error correction (FEC) scheme to generate an encoded signal, and a constellation mapper configured to modulate the encoded signal to symbol values according to a modulation scheme to generate a corresponding symbol stream for transmission through the communications system. The shaping operation reduces average constellation energy for constellations of the modulation scheme.

CROSS-REFERENCE

This application is a continuation of U.S. Ser. No. 15/616,997 filedJun. 8, 2017, which is itself a continuation of U.S. Ser. No. 13/917,339filed Jun. 13, 2013 (now U.S. Pat. No. 9,698,939 issued Jul. 4, 2017).The contents of both applications are incorporated herein by reference.

TECHNICAL FIELD

The present application relates generally to management ofcommunications systems, and more specifically to variable bandwidthoptical modulation schemes.

BACKGROUND

For achieving long distance optical signal transmission, at moderatespectral efficiencies, dual polarization Binary Phase Shift Keying(DP-BPSK) and coherent detection are commonly used. As is known in theart, BPSK encodes a single bit value (“0” or “1”) onto an opticalcarrier by modulating the carrier phase between two constellation pointsthat are separated by 180°. DP-BPSK achieves a spectral efficiency of2-bits per symbol period (baud), by independently modulating single bitvalues onto each of the orthogonal polarization modes of the opticalcarrier. This is illustrated in FIG. 1, which shows the BPSKconstellation mapped onto the Real (Re)-Imaginary (Im) plane of each ofthe X- and Y-polarizations.

As is known in the art, other modulation schemes enable increasedspectral efficiency by encoding increased numbers of bits per baud. Forexample, Quadrature Phase Shift Keying (QPSK) enables two bits to beencoded on each polarization, and thus four bits per baud for dualpolarization QPSK (DP-QPSK), by using a symmetrical 4-pointconstellation, as may be seen in FIG. 2. Other modulation schemes, suchas Quadrature Amplitude Modulation (QAM) achieve even higher numbers ofbits per baud by modulating both the phase and amplitude of the opticalfield. However, as the number of encoded bits-per-baud increases, theEuclidian distance between neighbouring constellation points decreases.For example, in the BPSK constellations shown in FIG. 1, eachconstellation point is separated from its neighbour by an anglecorresponding to 180° in the Re-Im plane. On the other hand, in the QPSKconstellations shown in FIG. 2, each constellation point is separatedfrom its neighbour by an angle corresponding to 90° in the Re-Im plane.The reduced separation between adjacent constellation points results ina corresponding decrease in system margin, which limits the maximumsignal reach.

Other things being equal, relative system margin varies inversely withthe number bits per baud, and both of these parameters are fixed by theencoding scheme. For example, FIG. 3 is a chart schematically showingthe relative system margin vs. bits-per-baud for DP-BPSK, DP-QPSK and16-QAM encoding schemes. In the example FIG. 3, DP-BPSK has the lowestspectral efficiency (2 bits-per-baud) but the highest system margin (andthus signal reach), whereas 16-QAM has the highest spectral efficiency(8 bits-per-symbol) but the lowest system margin.

For an optical communications system having a given baud rate, thespecific spectral efficiency and relative system margin of each encodingscheme translates into respective values of bandwidth and signal reach.Accordingly, a network service provider must select an encoding schemethat provides a combination of bandwidth and signal reach that mostnearly satisfies the anticipated demand, within the performancecapabilities of the network. However, this frequently leads tosub-optimal utilization of the network resources, because the selectedencoding scheme will almost invariably have lower spectral efficiencythan is permitted by the network performance in order to ensure adequatesystem margin. Furthermore, if the network service provider wants tochange the system margin, for example, they can only do so by changingthe encoding scheme. However, this can produce a large step-wise changein both system margin and spectral efficiency, which may also beundesirable.

Various known codes have been used in electrical systems to ensure aminimum number of transitions in a bit sequence. For example, 8B/10B isa line code that maps 8-bit symbols to 10-bit symbols to achieveDC-balance and bounded disparity, and yet provide enough state changesto allow reasonable clock recovery. This means that the differencebetween the count of 1 s and 0 s in a string of at least 20 bits is nomore than 2, and that there are not more than five 1 s or 0 s in a row.This helps to reduce the demand for the lower bandwidth limit of thechannel necessary to transfer the signal. Known scrambling techniquesmake this irrelevant in modern high speed fiber systems.

It is known that block shaping codes, such as the shell codes describedin Precoding and Signal Shaping for Digital Transmission; Robert F. H.Fischer; John Wiley & Sons, Inc., 2002, ISBN: 0-471-22410-3, can reducethe average power of the signal by adjusting the probability ofoccurrence of values of the bits, and efficiently encode fractional bitsper Baud. For example, the probability of a certain bit equaling 0 mightbe 0.75, and the probability of it equaling 1 would be 0.25. With PulseAmplitude Modulation (PAM), this reduces the average power transmittedby a factor of two. However, when decoding these blocks, one symbolerror can produce a large number of bit errors. At the symbol errorrates of modern fiber systems (on the order of 5%) this errormultiplication offsets the performance gains from the coding. If asymbol error results in a change in the number of bits out of the code,the resulting misalignment can cause a burst of 50% bit errors thatpersists for thousands of bits.

Forward Error Correction is a well-known method for reducing bit errorrates. However, the parity calculations for the added redundant bitsproduce an encoded signal in which the probability of any given bithaving a value of ‘1’ reverts to approximately 0.5, even when the inputbits deliberately have quite different probability distributions.

Trellis coding has been used in an attempt to overcome the problems oferror multiplication and reversion towards 0.5 probability. Symbol levelredundancy is included when shaping. Iterative Soft In Soft Out (SISO)decoding across the sequence of symbols is used to gradually reduce thesymbol error rate while decoding. This decoding would be verychallenging to implement with any significant performance improvement,at the high speeds and high noise levels of modern optical fibercommunications systems.

What is desired is a technique that enables spectral efficiency andsystem margin to be optimized.

SUMMARY

An aspect of the present invention provides a method of transmitting adata signal using an optical transmitter of an optical communicationssystem. An N/M mapping encoder processes an N-bit input vector inaccordance with a first mapping to generate a corresponding M-bit datastream. A Forward Error Correction (FEC) encoder processes the M-bitdata stream in accordance with a predetermined encoding scheme togenerate an encoded symbol stream. A modulator modulates a carrier lightin accordance with the encoded symbol stream to generate an opticalsignal for transmission through the optical communications system. Thefirst mapping can be adjusted to maximize performance of the opticalcommunications system.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the present invention will becomeapparent from the following detailed description, taken in combinationwith the appended drawings, in which:

FIG. 1 illustrates a DP-BPSK signal constellation in the Real(Re)/Imaginary (Im) plane;

FIG. 2 illustrates a DP-QPSK signal constellation;

FIG. 3 is a chart illustrating Relative System Margin and databits-per-baud characteristic of three encoding schemes known in the art;

FIG. 4 is a block diagram illustrating elements of an opticalcommunications system;

FIG. 5 is a block diagram illustrating elements of a transmitter inaccordance with a representative embodiment of the present invention;

FIG. 6 is a flow-chart illustrating a representative mapping methodusable in embodiments of the present invention;

FIG. 7 is a flow-chart illustrating a representative method forreversing the mapping of FIG. 6;

FIG. 8 is a chart illustrating Relative System Margin and databits-per-baud achievable using methods in accordance with the presentinvention; and

FIG. 9 is a diagram illustrating a tree code.

It will be noted that throughout the appended drawings, like featuresare identified by like reference numerals.

DETAILED DESCRIPTION

FIG. 4 illustrates a representative optical communication system inwhich techniques in accordance with the present disclosure may beimplemented. In the optical communication system of FIG. 4, atransmitter 2 generally comprises an encoder 4 for encoding a pair ofdata signals (Dx and Dy) to generate a set of drive signals 6. The drivesignals are then supplied to a modulator 8 for modulating respectivedimensions of a continuous wave (CW) optical carrier in accordance withthe drive signals. In the example of FIG. 4, a pair of data signals (Dxand Dy) may be encoded as 4 drive signals, which are then used tomodulate two dimensions (e.g. phase and amplitude, or I and Q) of eachorthogonal polarization of the optical carrier. The CW carrier istypically generated by a laser 10 in a manner known in the art, and themodulator may be implemented using any of a variety of known modulatordevices, such as phase modulators, variable optical attenuators,Mach-Zehnder interferometers etc. The modulated optical signal appearingat the output of the modulator is transmitted through an optical fiberlink 12 to a coherent receiver 14.

A receiver 14 configured to receive and detect the transmitted datasignals may be provided as a coherent receiver, which includes apolarization beam splitter 16 for splitting the received optical signalinto received X and Y polarizations, an optical hybrid 18 for separatelymixing the X and Y polarizations with a local oscillator, and a set ofphotodetectors 20 for detecting the optical power of each of the mixingproducts generated by the optical hybrid 18. An Analog to Digital (A/D)converter block 22 samples each photodetector current, and the resultingsample streams—each of which represents one of the modulated dimensionsof the optical carrier field—are processed by a Digital Signal Processor(DSP) 24 in accordance with the M-dimensional constellation to generaterecovered signals Rx and Ry that correspond with the transmitted datasignals Dx and Dy.

The present application provides techniques for transmitting the datasignals Dx and Dy with a variable spectral efficiency.

FIG. 5 illustrates a representative transmitter 26 implementingtechniques in accordance with the present invention. In the exampleembodiment of FIG. 5, the data signals Dx and Dy are supplied to an N/Mmapping encoder 28 which operates to map the data signals Dx and Dy to acorresponding pair of digital signals Sx and Sy using a mapping functiondescribed in greater detail below. The digital signals Sx and Sy outputfrom the N/M mapping encoder 28 are then supplied to a Forward ErrorCorrection (FEC) encoder 30 cascaded with a constellation mapper 32 anda driver 33 to generate drive signals 6 for modulating the opticalchannel lights in a conventional manner. At the receiver 14 (FIG. 4),the DSP 24 processes the sample streams output from the A/D block 22 togenerate first recovered signals corresponding to the digital signals Sxand Sy, and then reverses the mapping function of the N/M mappingencoder 28 to generate the recovered signals Rx and Ry that correspondwith the transmitted data signals Dx and Dy.

The driver 33 may operate in a manner known in the art to generateanalog drive signals 6 based on the symbol stream received from theconstellation mapper 32. In some embodiments, the driver 33 may includeone or more digital-to-analog circuits (DACs) along with appropriateanalog and/or digital signal processing circuits to performconditioning, scaling and filtering functions as needed to generatedrive signals 6 capable of driving the modulator 8 to modulate thecarrier light from the laser 10 to generate the desired optical signalat the output of the transmitter 26.

The FEC encoder 30 may operate to process the digital signals Sx and Syto calculate and insert parity bits using known techniques, which may beselected based on expected symbol error rates of the opticalcommunications system. The constellation mapper 32 may be used to mapthe FEC encoded signals to constellation point values in accordance witha selected modulation scheme. In general, the constellation mapper 32may be implemented using any suitable combination of hardware andsoftware. In some embodiments, the constellation mapper 32 may beimplemented using a Random Access Memory (RAM) Look-up table (LUT),which has an advantage in that such a mapper 32 is programmable. Thismeans that, for example, the modulation scheme and/or the value of eachconstellation point of the modulation scheme may be adjusted as desired.For example, a RAM can be divided into two or more pages, each of whichcontains a respective LUT for implementing the constellation mappingfunction. In such a case, the modulation scheme can be changed byloading an appropriate LUT into an unused page of the RAM, and thenselecting that page for use.

In some embodiments, the modulation scheme implemented by theconstellation mapper 32 may be selected to achieve maximum datatransmission speed through the link 12 under optimum conditions. Ifdesired, other equivalent criteria may be used, such as, for example,minimum permissible relative system margin under optimum conditions. Forexample, if the optical link can support 16-QAM modulation under optimumconditions, then the constellation mapper 32 may be designed to map theFEC-encoded signals from the FEC encoder 30 into symbols of a 16-QAMconstellation.

In general terms, the N/M mapping encoder 28 may comprise any suitablecombination of hardware and/or software to implement a mapping functiondesigned to reversibly map an N-bit input vector D into an M-bit outputvector S, where N and M are integer values, and N≤M. The input vector Dmay be considered to be a binary representation of a number having avalue between 0 and U=2^(N)−1. On the other hand, the output vector Smay be treated as a binary series of M bits; thus, S=s(1) . . . s(M).With this arrangement, the number of data bits per baud of the encodedsignals 6 output from the constellation mapper 32 can be varied bychanging the ratio N:M. This means that the relative system margin canbe adjusted to maximize performance of the communications system underthe typically sub-optimal conditions prevailing at any given time. Forexample, in the embodiment of FIG. 5, a controller 34 is connectedreceive a signal 36 indicative of a performance of the opticaltransmission link 12. In some embodiments, this signal 36 may comprisean indication of a performance parameter such as a bit error ratedetected at the receiver 14 (FIG. 4). The controller 34 may compare thesignal 36 to one or more predetermined thresholds, and operate to adjustthe mapping implemented by the N/M mapping encoder 28 to tune theperformance of the optical transmission link 12. An advantage of thistechnique is that the number of data bits per baud and the relativesystem margin can be adjusted without changing the modulation schemeimplemented by the constellation mapper 32. This means that it ispossible to achieve values of data bits per baud and relative systemmargin that are intermediate those associated with different modulationschemes.

As may be appreciated, as the ratio N:M is reduced, the likelihood of‘0’s in the binary series S generated by the N/M mapping encoder 28increases relative to the likelihood of ‘1’s. Unequal probabilities of‘0’s and ‘1’s in the binary series S may yield corresponding unequallikelihoods of different symbols in the encoded signals 6 generated bythe FEC encoder 30. In some embodiments, this may be used to alter thepower distribution of symbols in the encoded signals 6. For example, thebinary values assigned to each constellation point of the modulationscheme implemented by the constellation mapper 32 can be selected suchthat binary values having lower numbers of ‘1’s, or fewer transitionsbetween ‘0’ and ‘1’, are concentrated near the origin of the symbolconstellation. With this arrangement, as the number of ‘0’ increasesrelative to the number of ‘1’s in the binary series S, the proportion ofsymbols lying close to the origin will increase relative to symbols thatare further away from the origin. This may have the effect of alteringthe power distribution of encoded symbols in the output of theconstellation mapper 32. In some embodiments, a Gaussian powerdistribution of encoded symbols may be achieved.

In some embodiments, the mapping function has at least some of thefollowing properties:

I) The value of N should be a predetermined constant value that isindependent from the pattern of the information stream;

II) The value of M should be a predetermined constant value that isindependent from the pattern of the information stream;

III) The number of 0's (L) in the output data stream S should be apredetermined constant value that is independent of the pattern of theinformation stream. This property is specifically required forconstellation bit-labeling with variable bit length. Otherwise, it isrequired that the ratio of L:M, averaged across a plurality of inputvectors, is equal to a predetermined target probability level; and

IV) The mapping function should be reversible, meaning that no two inputvectors D can be mapped to the same output stream S.

When properties I and II above are satisfied, no single error in theinput of the N/M mapping encoder 28 will cause unbounded errorpropagation in the output of the N/M mapping encoder 28.

Property III above means that the respective probability of one elementof the output vector S is different from that of at least one otherelement. For example, the probability of a binary “1” in the outputvector S may be different from the probability of a binary “0”. In someembodiments, the un-equal probabilities may propagate through the FECencoder 30 to yield un-equal probabilities of the symbols of theconstellation in the drive signals 6. For example, when the probabilityof a binary “0” is larger than the probability of a binary “1” in theoutput vector S, the probability of higher energy symbols at the outputif the FEC encoder 30 may be lower than the probability of lower energysymbols.

FIG. 6 is a flow chart illustrating an example mapping function thatsatisfies each of the four properties described above. An advantage ofthe technique of FIG. 6 is that it can be readily implementing inhardware, which supports high-speed signal processing.

The algorithm of FIG. 6 starts with an N-bit input vector D andgenerates an M-bit output data stream S=s(k), k=1 . . . M viarecursively calculated values of an upper limit U(k), a Threshold TH(k),and a residue x(k).

At the start of the algorithm (e.g. k=1), the initial residue x(k)=D,and the initial Upper limit U(1)=2^(N)−1.

The threshold and upper limit can then be recursively calculated asfollows:

${{TH}(k)} = {\frac{B(k)}{\left( {1 + M - k} \right)}{U(k)}}$${U\left( {k + 1} \right)} = {{U(k)}\frac{\Delta_{k}}{\left( {M - k} \right)}}$$\Delta_{k} = \left\{ \begin{matrix}{B(k)} & {{{if}\mspace{14mu}{s(k)}} = 0} \\{M - k - {B(k)}} & {{{if}\mspace{14mu}{s(k)}} = 1}\end{matrix} \right.$

B(k) denotes the number of ‘0’s that remain between s(k) and s(M).Mathematically, B(k) may be represented as:B(k)=L+1+Σ_(j=1) ^(k=1) s(j)−k

Where L is the total number of ‘0’s in the output series S=s(k), k=1 . .. M. It will be seen that the initial condition, at k=1, B(k)=L.

During each iteration, the current output value s(k) and the nextresidue x(k+1) are calculated by comparing the current residue x(k) withthe threshold TH(k).

If (x_((k))≤TH(k)) and (TH(k)≠0), then s(k)=0 and x(k+1)=x(k)

Otherwise, s(k)=1 and x(k+1)=x(k)−TH(k)

The above process may iterate for each value of k=1 . . . M.

It can be easily verified that TH(1)>TH(2)>>TH(M); and thatU(1)>U(2)>>U(M).

Furthermore, for any value of k, the upper limit U(k)≥x(k), andU(k)≥TH(k).

As may be appreciated, the value of L defines a target number of “0”s inthe output data stream S. This value is proportional to a desiredprobability “p” that any given bit of the output data stream M is a “0”.During run-time, the threshold can be adjusted upwards or downwards, toensure that the actual proportion of “0”s in the output signal S closelymatches the desired probability “p”. In some embodiments, this can beaccomplished by monitoring the iterative process of FIG. 6 and trackingthe evolving proportion of “0”s in the output data stream S. If theevolving proportion rises above the desired probability “p”, then thethreshold TH can be reduced to thereby reduce the proportion of “0”sgenerated in subsequent iterations. Conversely, if the evolvingproportion drops below the desired probability “p”, then the thresholdTH can be increased to thereby increase the proportion of “0”s generatedin subsequent iterations.

Those of ordinary skill in the art will appreciated that this techniquecan be modified as desired to obtain suitable behaviours of thealgorithm. For example, if desired, the threshold TH may be adjusted tomaintain the proportion of “0”s in the output signal S above a desiredminimum value, or below a desired maximum value, or between some desiredmaximum and minimum value bounds.

In the receiver, the original N-bit input vector D can be reconstructedas:D=x(M+1)+Σ_(k=1) ^(M) s(k)TH(k)

For a fully reversible mapping function, it is necessary that the finalresidue x(M+1)<1. Furthermore, property III above requires that Σ_(k=1)^(M)s(k)=M−L. Both of these conditions can be satisfied by setting

${2^{N} \leq \begin{pmatrix}M \\L\end{pmatrix}},{{{where}\mspace{14mu}\begin{pmatrix}M \\L\end{pmatrix}} = {\frac{M!}{{L!}{\left( {M - L} \right)!}}.}}$In embodiments in which it is desirable to use the largest possiblevalue for N, it is preferable to also set

$2^{N} \leq \begin{pmatrix}M \\L\end{pmatrix} < {2^{N + 1}.}$An advantage of this arrangement is that the final residue x(M+1) is notneeded in order to reconstruct the N-bit input vector D. Rather, theinput vector D can be reconstructed as:D=┌Σ _(k=1) ^(M) s(k)TH(k)┐

Where ┌P┐ is the ceiling function on the real variable ‘P’.

FIG. 7 is a flow chart illustrating a representative process ofreconstructing the N-bit vector D from the M-bit data stream S=s(k), k=1. . . M. As may be seen in FIG. 7, at the start of the algorithm, theinitial values of k=1 and P=0 are set. During each iteration (k=1 . . .M), the corresponding values of U(k) and TH(k) can be calculated asdescribed above, and used to calculate the incremental value s(k)TH(k)that is added to the variable P. This iterative process is repeated foreach value of k until k=M+1, to accumulate a value of P. The value ofthe vector D can then be determined by calculating the ceiling functionof the accumulated value P.

As noted above, the presently disclosed technique enables the opticalcommunications system to operate with values of relative system marginand data bits per baud that are intermediate those associated withdifferent encoding schemes. This feature is illustrated by the dashedline in FIG. 8. As was also noted above, in some cases the mappingimplemented by the N/M mapping encoder 28 may also yield unequalprobabilities of each symbol of the encoding constellation, and this mayyield a Gaussian power distribution of the modulated optical signal. Insuch cases, the relative system margin for all possible values ofbits-per-baud may also be higher than that achieved using conventionalmethods. This is indicated in FIG. 8 by the dashed line lying above eachof the characteristic points of the three identified encoding schemes.

Another advantage of the methods described above with reference to FIGS.6 and 7 is that they are amenable to implementation in hardware, forexample using an Application Specific Integrated Circuit (ASIC) or aField Programmable Gate Array (FPGA). Hardware implementations aredesirable in that they enable the processing to be performed at highspeed, which reduces latency.

Further reductions in latency can be obtained by processing two or morevectors Dl . . . Dn using respective parallel processing paths. In someembodiments, each path may receive a respective vector D as a block of Ncontiguous bits of a data steam to be transmitted through thecommunications system. In other embodiments, each path may receive arespective N-bit vector D comprising interleaved bits from either two ormore data streams or two or more blocks of a common data stream.

An advantageous implementation of the constellation mapper 32 is amemory such as the LUT described in U.S. Pat. No. 7,386,240. The outputsdesirably include four dimensions, such as XI, XQ, YI, YQ, defining thedesired E-field. More dimensions can be used, such as the eight from twotime-slots of a dual polarization system. It is advantageous that theoutputs are filtered or further processed before being passed to thedriver 33 that drives the optical modulator 8. Fewer input bits to thelookup table might be used, or fewer dimensions output. The programmableaspect of the lookup table is advantageous for supporting a variety ofmodulations. A minimalist version of this function may merely organizethe input bits of a symbol and connects them to a downstream unit suchas a filter, DAC, or output driver, with no programmable flexibility.

In an alternative embodiment, the N/M mapping encoder 28 may implement ashell code such as described by Fischer (supra).

In a further alternative embodiment, the N/M mapping encoder 28 mayimplement a tree code. Tree codes (which are a super-set of shell codes)can achieve shaping gain and other desirable properties such asbalancing the power or the polarization within a chosen time interval. Afurther benefit of tree codes is that they can be efficientlyimplemented in hardware, which enables their use in high baud ratecommunications systems. FIG. 9 illustrates a representative tree code.As may be seen in FIG. 9, the tree comprises a plurality of nodes 38,each of which has an input and two outputs. In the illustratedembodiment, the nodes 38 are arranged in layers 40. The nodes 38 of eachlayer 40 also receive a corresponding bit (D(x)) of the N-bit inputvector D. The M-bit data stream is output via the “leaves” of the tree(which appear at the bottom of the illustration of FIG. 9). Each node 38may implement a memoryless logical operation which divides any energyreceived via its input (e.g. from a node in the previous layer) betweeneach of its two outputs, based on the value of the received vector bitD(x). Since the logical operation implemented by each node is bothmemoryless and known, the encoding implemented by the tree can bereliably reversed to recover the input vector D from the M-bit datastream.

Shaping gain allows reduced average power for a given coding rate andgiven noise tolerance. Equivalently, the shaping gain allows anincreased signal to noise level for a given coding rate and averagepower.

With block coding, the rate can be set to the desired value, such as therational number R=p/q p is a function of the number of input bits to theblock and q is function of the number of output bits per block and thenumber of output bits encoded in each Baud or in each dimension.Preferably, p and q are relatively prime, which in this technique meansthat they are selected such that they do not share any common factors(except ‘1’). If q=1 then R is an integer. Typical such values of p/qare 73/64, 69/128, 551/256, or 7999/5192 bits per dimension.

The ability to have fine granularity in the control of the rate R (e.g.bits per dimension) as compared to an integer granularity, allows R tobe adjusted so as to just achieve the required noise tolerance withouthaving to round R down to an integer. Given that the integer rate isgenerally one or two bits per dimension, the wasted fraction has a largeimpact.

The output of the outer shaping code is a set of bits or symbols thathave unequal probability distributions or may have dependence acrosstime in the same block. Systematic forward error correction is applied,so that the output is the original bits (or symbols) and additionalsyndrome bits (or symbols). BCH product codes, large block Low DensityParity Code (LDPC) codes, or block turbo codes are advantageous FECmethods.

The resulting bits (or symbols) are used to address a constellationmapper that produces the digital representation of the complex dualpolarization E-field that, after appropriate filtering, is approximatedby the output of the optical modulator.

In some constellation mappings, one can separate the bits into two sets:sign bits and magnitude bits. The distinction between the sets is that agreater optical transmission performance improvement is made by havingmagnitude bits with a probability of the occurrence of a ‘1’ being otherthan 0.5, than by having sign bits with a probability of the occurrenceof a ‘1’ being other than 0.5. Distinguishing these sets allows shapingand other bit-probability varying methods to have greater effect. In theexample below, the sign and magnitude bits literally correspond to signsand magnitudes of the modulation, hence their names, but in general theonly requirement is the set distinction.

The above-described techniques can support modulation formats with morethan 1 magnitude bit for any constellation point. Since the N/M mapping,FEC encoding scheme and the modulation format implemented by theconstellation mapper 32 are all known in detail, it is possible use themapping function implemented by the N/M mapping encoder 28 to producedifferent symbol probabilities for different symbols in the symbolstream output from the constellation mapper 32. For example, theprobability of the second magnitude bit of each symbol being “0” can bechanged depending on the value of the first magnitude bit of the samesymbol. In the corresponding embodiments, we will have two parallelflows of bits being processed in accordance with the flowchart of FIG. 6where in the first flow the second magnitude bit is generated with aspecific probability distribution corresponding to the first magnitudebit being “0” while in the second flow, the second magnitude bit isgenerated with another specific probability distribution correspondingto the first magnitude bit being “0”.

By means of the above method, it is possible to select just a subset ofthe symbol constellation by assigning the probability of other symbolsto “0”. The subset can be selected based on properties such as Euclideandistance between constellation points, average power, or nonlinearinterference, as desired.

In general, magnitude bits might indicate a desired physical property ofthe optical signal as well. Examples of such physical properties arepower or polarization state (i.e. stokes state vector). For thoseapplications, the probability distribution of symbols can be devisedsuch that the desired physical property is kept in an appropriate rangein a block of consecutive symbols. Examples of that are keeping theaverage power between one or many consecutive symbols in a desirablerange and/or keeping the average polarization state between one or manyconsecutive symbols in a desirable range.

It is desirable to use the systematic bits to address a desired aspectsuch as magnitude or polarization state of the constellation, and thesyndrome bits to address the sign or phase aspects. For example, if themodulation is 8-PAM per dimension there are two magnitude bits and onesign bit per dimension. All of the syndrome bits become sign bits, andall of the magnitude bits come from systematic bits. (A few left oversystematic bits could become the left over sign bits.) With thisaddressing, most of the shaping created by the shaping code is preservedin the optical modulation, and the required degree DC balance ispreserved because each sign bit has a probability of ½ of having a valueof one.

After transmission over the fiber, the receiver detects the bits (orsymbols) and passes them to the FEC. If the chosen FEC is a softdecision FEC, a confidence metric such as a log-likelihood ratio iscalculated for each bit or symbol. The large block FEC has an outputframe error rate that is much less than about 10⁻¹², in the operatingregime. With the probability of an error in the frame beingapproximately zero, the error multiplication effect is no longer aperformance impediment, and the full shaping gain, and fractional rategain is achieved.

The embodiments of the invention described above are intended to beillustrative only. The scope of the invention is therefore intended tobe limited solely by the scope of the appended claims.

What is claimed is:
 1. A method of transmitting a binary data signalusing a transmitter of a communications system, wherein the bits of thebinary data signal have a probability of being a ‘1’ substantially equalto 0.5, the method comprising: applying a shaping operation to thebinary data signal to generate a shaped data signal, the shapingoperation creating a plurality of shaped bits with a probability ofbeing a ‘1’ other than 0.5; calculating a parity equation based at leastin part upon a first shaped bit; and choosing a symbol to transmit, thechoice of amplitude of the symbol being based at least in part upon asecond shaped bit, wherein a sign of the symbol is based at least inpart upon the parity equation, and the probability that the sign of thesymbol is positive is substantially equal to the probability that thesign of the symbol is negative.
 2. The method as recited in claim 1,wherein the communications system is an optical communications system,the method further comprising modulating a carrier light according tothe chosen symbol to generate an optical signal for transmission throughthe optical communications system.
 3. A transmitter of a communicationssystem, the transmitter comprising: a first encoder configured to applya shaping operation to a binary data signal to generate a shaped datasignal, wherein the bits of the binary data signal have a probability ofbeing a ‘1’ substantially equal to 0.5 and the shaping operation createsa plurality of shaped bits with a probability of being a ‘1’ other than0.5; a second encoder configured to calculate a parity equation based atleast in part upon a first shaped bit; and a constellation mapperconfigured to choose a symbol to transmit, the choice of amplitude ofthe symbol being based at least in part upon a second shaped bit, wherea sign of the symbol is based at least in part upon the parity equation,and the probability that the sign of the symbol is positive issubstantially equal to the probability that the sign of the symbol isnegative.
 4. The transmitter as recited in claim 3, wherein thecommunications system is an optical communications system, thetransmitter further comprising a modulator configured to modulate acarrier light according to the chosen symbol to generate an opticalsignal for transmission through the optical communications system.
 5. Amethod of transmitting a data signal using a transmitter of acommunications system, the method comprising: applying a shapingoperation to the data signal to generate a shaped data signal; encodingthe shaped data signal according to a forward error correction (FEC)scheme to generate an encoded signal; and modulating the encoded signalto symbol values according to a modulation scheme to generate acorresponding symbol stream for transmission through the communicationssystem, wherein the shaping operation reduces average constellationenergy for constellations of the modulation scheme.
 6. The method asrecited in claim 5, further comprising modulating a carrier according tothe symbol stream to generate a signal for transmission through thecommunications system.
 7. The method as recited in claim 5, whereinencoding the shaped signals according to the FEC scheme and modulatingthe encoded signal to symbol values according to the modulation schemesubstantially preserves the reduction in average constellation energy.8. The method as recited in claim 5, wherein the shaping operationcomprises probabilistic shaping.
 9. The method as recited in claim 8,wherein each symbol comprises one or more dimensions and the shapingoperation alters the probability distribution of the amplitude of adimension in the symbol stream while substantially preserving the signof the dimension.
 10. The method as recited in claim 9, wherein the signof the dimension is substantially determined by overhead bits generatedby the FEC encoding.
 11. The method as recited in claim 5, wherein thecommunications system is an optical communications system and modulatingthe encoded symbol comprises modulating light according to the symbolstream to generate an optical signal for transmission through theoptical communications system.
 12. A transmitter of a communicationssystem, the transmitter comprising: a first encoder configured to applya shaping operation to a data signal to generate a shaped data signal; asecond encoder configured to encode the shaped data signal according toa forward error correction (FEC) scheme to generate an encoded signal;and a constellation mapper configured to modulate the encoded signal tosymbol values according to a modulation scheme to generate acorresponding symbol stream for transmission through the communicationssystem, wherein the shaping operation reduces average constellationenergy for constellations of the modulation scheme.
 13. The transmitteras recited in claim 12, further comprising a modulator to modulate acarrier according to the symbol stream to generate a signal fortransmission through the communications system.
 14. The transmitter asrecited in claim 12, wherein encoding the shaped signals according tothe FEC scheme and modulating the encoded signal to symbol valuesaccording to the modulation scheme substantially preserves the reductionin average constellation energy.
 15. The transmitter as recited in claim12, wherein the shaping operation comprises probabilistic shaping. 16.The transmitter as recited in claim 15, wherein each symbol comprisesone or more dimensions and the shaping operation alters the probabilitydistribution of the amplitude of a dimension in the symbol stream whilesubstantially preserving the sign of the dimension.
 17. The transmitteras recited in claim 16, wherein the sign of the dimension issubstantially determined by overhead bits generated by the FEC encoding.18. The transmitter as recited in claim 12, wherein the communicationssystem is an optical communications system, the transmitter furthercomprising a modulator to modulate light according to the symbol streamto generate an optical signal for transmission through the opticalcommunications system.